C. de Dominicis and I. Giardina: Random fields and spin glasses: a field theory approach

Abstract

The Wilsonian field theoretic approach has made its important and lasting mark on the theory of critical phenomena. Many heavy tomes have been dedicated to its mastery and explanation of its baroque details. This book comes on the wake of the Wilsonian revolution and deals with the intricacies of applying the field theoretic methods to the analysis of disordered systems, most notably the Random Field Ising Model and the Ising Spin Glass. It is written in masterly and elegant fashion by two remarkable researchers who have themselves, in particular prof. De Dominicis, fundamentally contributed to the subject. It is definitely not an introductory book, assumes a detailed knowledge of the field theory, and as such I can only recommend it either to researchers already working on disordered systems or advanced graduate students and postdocs. The authors masterly wield the various methods of field theory in order to “clarify and unify” via its mathematical language some of, in their opinion, more cryptic and pointed details of the theory of disordered systems. As already stated, this is not an introductory book but it is an interesting treatise on the intricacies of the various advanced and little known methods and techniques of the field theory, that can be applied to the various aspects of the theory of disordered systems. The book grew out of a set of lectures delivered by Prof. De Dominicis at Saclay and Porto Alegre that later grew into a book with the participation of his postdoc, Irene Giardina. The focus of this book are the unifying features of the disordered systems that can be adequately represented within the field theoretic language. The book is not exhaustive but represents rather a set of beautiful formal vignettes on some aspects of the field theoretic approach to disordered systems that do not require too much space and do not completely exhaust the reader with arcane details, but are never really very far from this. It is written in lapidary style and tells just enough to provide a meaningful framework for the formal developments. A typical example of its style being the first chapter, “A brief introduction”, that sets down the basics of the disordered systems in seven pages starting with quenched